The White House urged Congress Tuesday to quickly approve free-trade agreements with South Korea, Colombia and Panama, after a deal was struck with lawmakers to restore benefits for job losses related to trade.

"Now it is time to move forward with TAA and with the Korea, Colombia, and Panama trade agreements, which will support tens of thousands of jobs," said White House Press Secretary Jay Carney in a statement.

The hard-won agreement to renew Trade-Adjustment Assistance is expected to clear the way for all three trade deals to win passage in Congress, though the top Republican in the Senate warned that linking the worker retraining program to the trade pacts could cause defections in his party. Sen. Mitch McConnell (R., Ky.), said not allowing a separate vote on Trade-Adjustment Assistance "puts at risk what should be a bipartisan job-creation exercise."

As reported by The Wall Street Journal, under a bipartisan compromise, renewing the funding for worker retraining will be included in legislation to implement the South Korea trade pact in the Senate, according to people familiar with the situation.

Reviving expired programs giving duty-free access to Andean nations and a host of developing countries will also be part of the package, though the overall process on how all the trade measures are to be tied together is still being worked out in the House.

Senate Finance Committee Chairman Max Baucus (D-Mont.) announced plans to begin informal debate on the trade deals Thursday, which is the last opportunity for congressional input before they are submitted for an up-or-down vote.

"We think this package can get the support needed to become law. American workers and our economy can't afford for us to wait any longer to move forward," said Baucus.

(Corey Boles and Elizabeth Williamson contributed to this story)